Trees are a unique hazard. Normally with water or bunkers anyone can try to play closer to them in order to gain a strategic advantage. In fact there is usually an advantage for even a short but accurate player to play toward this type of hazard (a long, accurate player will benefit perhaps even more). Trees are different. If a short but accurate player plays closer to the trees on the hole in the original post, he might be stymied. To take advantage of playing close to the trouble, you also need to be long enough to get past it. This is a common situation with trees. This is their nature, they are an aerial hazard. Unlike bunkers and water they interfere with the flight of the ball as well as the stance and swing.
With how far and (more importantly) how high good players hit the ball these days, trees are one of the few ways to make them have to curve and flight their ball. There just aren't many ground contours severe enough to force players to curve the ball considering how high they hit it.
In that sense, trees are sometimes less a test of strategy and more a test of skill (there are elements of both strategy and skill in any kind of hazard though). However, it is a skill that most feel is important and needs to be preserved and tested.
Trees are certainly over-used, often to the point of removing the intended strategy of the hole. But that doesn't meet they can't be used properly, or that we shouldn't encourage their proper use.